They cannot remain outside; they'll have to be houseplants, but they usually aren't treated this way (kept more than a season), so we don't know how well they'll adapt. Some gardeners have success keeping them barely alive until they can go back outside in May, while others have lost the plants. If you decide not to cut the stems back (possibly the better option, but we don't really know how much it matters), the peppers would need to be kept either in direct sun in a bright window, or grown under plant grow lights. Don't prune the roots. One issue is the inherently low ambient humidity indoors during winter, which can stress most types of indoor plants that prefer higher levels. A room humidifier might help in that case, or grouping plants together. Let the potting mix get slightly dry for the top inch or two before watering thoroughly, and if the plant sits on a saucer, empty it after watering so the drained water doesn't seep back into the pot, which might drown roots. Peppers don't have a good tolerance for prolonged soil sogginess.

Keep an eye out for indoor plant pests like spider mites, thrips, mealybugs, and aphids, all of which could be accidentally brought in on the plants. They might hide-out on the leaf undersides or in crevices like where the leaves connect to the stem.

Miri